Assessment of Low Probabilities of Failure by Extrapolation

This presentation was made at the 2019 NAFEMS World Congress in Quebec Canada

Resource Abstract

Reliability analysis focuses on the Probability of Failure (PoF). A safe structure implies a low PoF; however, sometimes the PoF is too low to calculate. The analysis produces a distribution of probabilities, but failure lies outside the range of calculated values. Especially in those cases where reliability analysis is of utmost importance, it is detrimental that the calculation of the PoF fails. The PoF can be estimated with extrapolation from available results. However, the distribution of probabilities shows a tail with a fast decreasing slope. Therefore, extrapolation from this tail is inaccurate.

An alternative is to use the reliability index, Beta. Because the relationship between failure and Beta is much more gradual, extrapolation from this function is much more accurate.

This method is applied to a simple beam model, and the extrapolation is based on a linear fit. Because the extrapolation is realized by a linear function, the resulting PoF is very accurate. Furthermore, the linear fit can be transformed back to the distribution tail. The extrapolation function follows the fast decreasing slope accurately.

Since the proposed method offers the possibility to estimate an accurate PoF it establishes a sound approach of reliability analysis when low probabilities are involved. Hence, the extrapolation based on the reliability index offers a valuable method to estimate the PoF.